Research map / Learning theory and algorithms / Matrix and tensor methods
Gaussian process nonparametric tensor estimator and its minimax optimality
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Linear kernel GP (ours) vs scaled latent convex regularization on Restaurant data | Gaussian process tensor estimator · Restaurant data | MSE | Helped |
| Gaussian process with GRBF kernel vs ALS on Restaurant data | Gaussian process tensor estimator · Restaurant data | MSE | Helped |
| Adding a linear kernel to a mixture with GRBF kernels (mixture beyond 2000 samples) (ablation) | Gaussian process tensor estimator · Restaurant data | MSE | Helped |
| Side information kernel on shops (anti-similarity Euclidean commute-time kernel) vs no side information (delta kernel) (ablation) | Gaussian process tensor estimator · Online shopping sales | MSE | Helped |
| Linear kernel for GP on latent factors vs GRBF kernel on online shopping data (ablation) | Gaussian process tensor estimator · Online shopping sales | MSE | Hurt |
| Scaled latent convex regularization baseline on School data | scaled latent · School data | explained variance | Hurt |
| Scaling Gaussian process prior by learned scale lambda (adaptive scale) to reach optimal rate | Gaussian process tensor estimator · theory (convergence rate) | convergence rate | Helped |
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- Minimax Optimal Alternating Minimization for Kernel Nonparametric Tensor Learning (NeurIPS 2016 · similarity 0.89)
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- Nonparametric Decomposition of Sparse Tensors (ICML 2021 · similarity 0.88)
- Efficient Nonparametric Tensor Decomposition for Binary and Count Data (AAAI 2024 · similarity 0.87)
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